In the development of oil and gas fields, it is common to quantify hydrocarbon fluid flow and transport using a reservoir simulator. For example, ECLIPSE™ (a trademark of Schlumberger) is an oil and gas reservoir simulator that provides a high resolution reservoir model that simulates fluid flow and mass transport in highly complex, variably saturated conditions. ECLIPSE, which is described in co-owned U.S. Pat. Nos. 6,018,497, 6,078,869 and 6,106,561 which are hereby incorporated by reference herein in their entireties, can couple geomechanical modeling with fluid flow. ECLIPSE can also perform fluid flow predictions. Other simulators similarly model fluid flow in formations during production.
ECLIPSE and other simulators typically utilize the well-known continuity equation based on Darcy's law that has been broadly used by reservoir engineers of the oil and gas industry for many years with various degrees of success. The great boom story of North America shale gas exploitation has seen an extension of the use of the same continuity equation from the simulation of conventional gas reservoirs to the simulation of unconventional reservoirs containing formation matrices of extremely-low permeability and extremely small pore sizes imbedded with highly conductive hydraulic fractures. While the continuity equation is being used in these unconventional reservoirs, the limitations of the continuity equation with respect to unconventional reservoirs have been documented. The issue is further complicated by the existence of highly permeable hydraulic fracture of fracture network in an extremely low permeable reservoir. At the center of the issue is the validity or accuracy of the Darcy's law in quantifying gas transport both in low permeability formation matrix and through highly permeable fractures.